Optimal Multi-Robot Path Planning with LTL Constraints: Guaranteeing Correctness through Synchronization

In this paper, we consider the automated planning of optimal paths for a robotic team satisfying a high level mission specification. Each robot in the team is modeled as a weighted transition system where the weights have associated deviation values that capture the non-determinism in the traveling times of the robot during its deployment. The mission is given as a Linear Temporal Logic (LTL) formula over a set of propositions satisfied at the regions of the environment. Additionally, we have an optimizing proposition capturing some particular task that must be repeatedly completed by the team. The goal is to minimize the maximum time between successive satisfying instances of the optimizing proposition while guaranteeing that the mission is satisfied even under non-deterministic traveling times. After computing a set of optimal satisfying paths for the members of the team, we also compute a set of synchronization sequences for each robot to ensure that the LTL formula is never violated during deployment. We implement and experimentally evaluate our method considering a persistent monitoring task in a road network environment.